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Seminar Details

Too Acute to be True?

  • Start Date: October 14, 2020
  • Event Start Time: 12:15 PM
  • Event End Time: 1:15 PM
  • Seminar Series: Graduate Combinatorics Seminar
  • Presenter(s): Quentin Dubroff - Rutgers University
  • Event Location: Online Event
  • Event Additional Info: <p>Presented via Zoom:&nbsp;<a href="https://nam02.safelinks.protection.outlook.com/?url=https%3A%2F%2Frutgers.zoom.us%2Fj%2F98441409199&amp;data=02%7C01%7C%7C5c0dff3070f84d8a170a08d864acb574%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C0%7C637370040219239080&amp;sdata=XomEVUCot4Act%2BOIGWERoDqmFvDdK2VpLP1zhZn2MVs%3D&amp;reserved=0" target="_blank">https://rutgers.zoom.us/j/98441409199</a></p> <p>Password: 715004</p> <p>&nbsp;</p> <p>See:&nbsp;<a href="https://sites.math.rutgers.edu/~qcd2/GCS.html" target="_blank">https://sites.math.rutgers.edu/~qcd2/GCS.html</a></p>
  • Presentation Type: Stand Alone Presentation
  • Abstract:

    Let f(d) be the maximum number of points in R^d such that every three form an acute triangle. For decades, it was thought that f(d) should grow linearly until a striking application of the probabilistic method by ErdÅ‘s and Füredi showed that f(d) grows like C^d for some C>1. A few tiny improvements were made on this until very recently when a series of papers showed that f(d) is at least 2^{d-1}, nearly matching the upper bound of 2^d. I will recount this story, highlighting a few of the most clever arguments, as well as discuss its connection to a problem in coding theory which remains wide open.